Model predictive control (MPC) has established itself as a promising control methodology in power electronics. This survey paper highlights the most relevant MPC techniques for power electronic systems. These can be classified into two major groups, namely, MPC without modulator, referred to as direct MPC, and MPC with a subsequent modulation stage, known as indirect MPC. Design choices and parameters that affect the system performance, closed-loop stability and controller robustness are discussed. Moreover, solvers and control platforms that can be employed for the real-time implementation of MPC algorithms are presented. Finally, the MPC schemes in question are assessed, among others, in terms of design and computational complexity, along with their performance and applicability depending on the power electronic system at hand.